A finite element implementation of finite deformation surface and bulk poroelasticity

TL;DR

This paper develops a finite element model for coupled surface and bulk poroelasticity at finite strains, crucial for understanding biological and miniaturized systems where surface effects are significant.

Contribution

It introduces a thermodynamically consistent formulation and finite element implementation for fully coupled surface and bulk poroelasticity at finite deformation, addressing a gap in existing methods.

Findings

Captures interplay between deformation and diffusion in bulk and surface.

Provides insights into surface effects in soft hydrated solids.

Enables study of biological and miniaturized systems with coupled processes.

Abstract

We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on surface. Nonlinear theories allow us to systematically study porous solids in a wide range of applications, such as drug delivery, biomaterial design, fundamental study of biomechanics and mechanobiology, and the design of sensors and actuators. As we aim to understand the physical phenomena at a smaller length scale towards comprehending the fundamental biological processes and the miniaturization of devices, the surface effect becomes more pertinent. Although existing methodologies provide the necessary tools to study coupled bulk effects for deformation and diffusion; however, very little is known about fully coupled bulk and surface poroelasticity at finite strain. Here we develop a thermodynamically consistent formulation for multiphysics processes of surface and bulk poroelasticity, specialized for soft hydrated solids, along with a corresponding finite element implementation. Our multiphysical approach captures the interplay between competing processes of finite deformation and species diffusion through the bulk and surface, and provides invaluable insight when surface effects are important.